McCabe-Thiele separation method

Apply the McCabe-Thiele graphical method to determine the number of equilibrium stages required for a given separation and the optimal location along the cascade for introduction of the feed. 

The conventional McCabe-Thiele graphical method for analysis of binary mixtures was applied to determine the number of theoretical plates necessary for the separation, 11,3 theoretical plates are required for the rectifying section, and 9.4 for the stripping section. Thus a total of 20,7 theoretical plates are required. Since the value of chosen was 70 per... 

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

The number of stages required for a given separation can be determined from the triangular diagram using a method analogous to the McCabe-Thiele diagram used to determine the... 

The reduction in the required number of plates as R is increased beyond Rm will tend to reduce the cost of the column. For a column separating a benzene-toluene mixture, for example, where Xf = 0.79, xd = 0.99 and xw = 0.01, the numbers of theoretical plates as given by the McCabe-Thiele method for various values of R are given as follows. The minimum reflux ratio for this case is 0.81. 

For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction yA in the vapour depends not only on X/ in the liquid, but also on the relative proportions of the other two components. 

The cascade can be drawn graphically in the McCabe-Thiele form, but the equilibria are so distorted that the exercise is not very valuable. This is a general finding in industrial practice. Graphical methods are adequate to give an indication of the number of stages likely to be needed for a particular duty. They fail when separations between similar species are sought. 

The separation analysis by established methods of McCabe -Thiele or Ponchon Savarit are compared with a flow sheeting program ASPEN+. It will be demonstrated, that a reliable scale -up is possible combining all these methods. 

Established methods like McCabe-Thiele or Ponchon-Savarit may be used to compute the number of theoretical stages for a given separation. Both methods are limited to a binary... 

Annual cost for distillation column. The McCabe-Thiele simplifying assumptions apply for this case, and the number of theoretical plates can be determined by the standard graphical method shown in Fig. 11-8. The slope of the enriching operating line is 1.5 /(1.5 + 1) = 0.6. From Fig. 11-8, the total number of theoretical stages required for the given separation is 12.1. 

Design a distillation column to separate benzene, toluene, and xylene, using (1) the McCabe-Thiele xy diagram and (2) the Fenske-Underwood-Gilliland (FUG) method. Compare the results with each other. Assume that the system is ideal. 

The plot at right shows points taken from the operating lines in the rigorous ChemSep separation and compares them with the ROL and SOL calculated using the McCabe-Thiele method. These calculated operating lines are the straight, solid lines on the plot. 

The separation of a binary mixture by distillation may be represented in two-dimensional space while n-dimensional space is required to represent the separation of a multicomponent mixture (i > 2). The graphical method proposed by McCabe and Thiele9 for the solution of problems involving binary mixtures is presented in a subsequent section. The McCabe-Thiele method makes use of an equilibrium curve which may be obtained from the boiling-point diagram."... 

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